Packet Scheduling: Weighted Fair Queueing (WFQ) ( ) and Virtual - - PowerPoint PPT Presentation

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Packet Scheduling: ( ) Weighted Fair Queueing (WFQ) and Virtual Clock (VC) and Virtual Clock (VC)

2/2/2017

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Fair Queueing server

R Flow 1 packets Flow 2 packets R Flow n packets

1.

Round robin service



Packet by packet round robin



Packet-by-packet round robin

• 2. Processor sharing



Each flow receives a service rate of R/n



Each flow receives a service rate of R/n, where R is channel rate in bps and n is the number of flows with non-empty queue

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Weighted Fair Queueing (WFQ) server

w1 w2 R Flow 1 packets Flow 2 packets wn Flow n packets

 Each flow i is given a weight wi  Service rate received by flow i is  Service rate received by flow i is ri = R * wi / (w1 + w2 + ... + wn) where R is channel rate in bps where R is channel rate in bps

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Fluid Flow System (Processor Sharing) F F y m ( g)

 Assume work-conserving server with no

scheduling overhead scheduling overhead

 Processor sharing can be implemented  Processor sharing can be implemented

(conceptually) using bit-by-bit weighted round robin robin

During each round, each flow with data sends a

number of bits proportional to the flow’s weight

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Fluid Flow Example

Packet Size (bits) Packet inter-arrival time (ms) Arrival Rate (Kbps) Fl 1 1000 10 100

100 Kbps Flow 1 (w1 = 1)

Flow 1 1000 10 100 Flow 2 500 10 50

Flow 2 (w2 = 1)

Flow 1 arrivals

1 2 3 4 5

Note: Each number is one packet

Flow 2 arrivals Time Time

1 2 3 4 5 6

packet

1 2

3 1 2 4 3 4 5 5 6 Time Service in fluid flow 1 2 3 4 5 6 in fluid flow system Time (ms) 10 20 30 40 50 60 70 80

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Packet-by-packet system Packet by packet system

 bit-by-bit round robin is not practical

1 2

3 1 2 4 3 4 5 5 6 Service in fluid flow system time (ms)

 Idea: Use finishing time of packet in fluid

system as priority for choosing the next

1 2 1 3 2 3 4 4 5 5 6

Packet-by-packet system

packet for service

system time (ms)

Note: Each number is one packet

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Packet finishing time

 Define



finishing time of packet j in flow f

( )

f

L j



finishing time of packet j in flow f



arrival time of packet j in flow f



length (in bits) of packet j in flow f

( )

f

s j

( )

f

A j ( ) L j

g ( ) p j f  Suppose

is a constant service rate (bits/sec) allocated to flow f

( ) j

f

r

allocated to flow f

Then the finishing time of packet j+1 in flow f

would be

( 1) ( 1) m ax{ ( ), ( 1)}

f f f f f

s j L j L j A j r + + = + +

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However

In WFQ the service rate received by In WFQ, the service rate received by each flow changes whenever a new flow arrives flow arrives

 When this happens, the finishing times

• f packets change and will need to be
• f packets change and will need to be

recomputed

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Solution: Virtual Time, V(t) Solut on V rtual T me, V(t)

 V(t) is the round number in the bit-by-bit

round robin system round robin system

 Observation: When a packet of a new flow

arrives an existing packet’s finishing time in arrives, an existing packet s finishing time in round number does not change

 thus, finish order of existing packets does not

, g p change  Instead of a packet’s finish time, compute

the round # when a packet will finish (virtual time finishing time)

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Virtual Time, V(t) (cont.) ( )

 V(t) increases inversely proportionally to the

sum of the weights of the backlogged flows

Flow 1 (w = 1) Flow 2 (w2 = 1) Flow 1 (w1 = 1)

time time

1 2

3 1 2 4 3 4 5 5 6

C C/2

V(t)

(round #)

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time t

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WFQ/PGPS scheduling

 Define



virtual time finishing time (in round number)

( )

f

P j



virtual time finishing time (in round number)

• f packet j in flow f



arrival time of packet j in flow f

( )

f

A j ( ) P j

p j f



length (in bits) of packet j in flow f



weight (in bits) of flow f

( )

f

s j

( ) j

f

w

The priority of packet j+1 in flow f is its virtual

time finishing time

( 1)

f f f f

s j +

 Select the packet with smallest priority for

( 1) ( 1) m ax{ ( ), ( ( 1))}

f f f f

s j P j P j V A j w + + = + +

service

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PGPS delay relative to GPS PGPS delay relat ve to GPS

Let ( ) denote the departure time of packet

PGPS

L i i for packet-by-packet WFQ service Let ( ) denote the departure time of packet

GPS

L i i for bit-by-bit WFQ service

Parekh and Gallager (1993) proved

max

Parekh and Gallager (1993) proved ( ) ( )

PGPS GPS

L i L i v ≤ +

No notion of a reserved rate nor admission control that

max

where is maximum packet service time v

No notion of a reserved rate, nor admission control that bounds the number of flows

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Virtual Clock scheduling [L Zhang 1990] Virtual Clock scheduling [L. Zhang 1990]

 A flow f is allocated a reserved service

rate, rf, similar to TDM

 but unlike TDM, if a flow idles, its reserved

t b d b th fl rate can be used by other flows  Like TDM, however, there are “firewalls”

between individual packet flows i e between individual packet flows, i.e.

 A flow source that generates packets at a rate

much higher than its reserved rate, may take mu g n , m y up idle capacity

 but it cannot affect the throughput rates

t d t th fl guaranteed to other flows

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Virtual Clock server

 Each flow f has a “virtual clock”, priority(f),

which is zero initially and updated whenever a new packet in flow f arrives packet in flow f arrives

 Let p denote a packet in flow f, with length l(p)

p p , g (p) bits and arrival time, A(p) ( ≥ 0). Upon its arrival,

( ) l p

The new value of priority(f) is assigned to packet

( ) ( ) max{ ( ), ( )}

f

l p priority f priority f A p r ← +

The new value of priority(f) is assigned to packet p as its virtual clock value, denoted by P(p)

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Virtual Clock server (cont.)

 priority (f) holds the virtual clock value of

the most recent packet arrival of flow f the most recent packet arrival of flow f

 Virtual clock values of packets are determined

by the sequence of packet arrival times and their service times  Whenever the server is ready for another

k t th k t m ll fl s ith th packet, the packet among all flows with the smallest virtual clock value is selected

 FCFS within a flow  FCFS within a flow  non-preemptive

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Properties of VC server

 Each flow f is allocated a reserved service

rate, rf

 The number of flows is limited (admission

control)  A misbehaving flow source that generates

packets at a rate higher than its reserved packets at a rate higher than its reserved rate, may take up idle capacity

 but it cannot affect the throughput rates

ff g p guaranteed to other flows

No consideration of delay guarantee or bound in the original paper

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No consideration of delay guarantee or bound in the original paper

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References References

 A. Demers, S. Keshav, S. Shenker, “Analysis and

simulation of a fair queueing algorithm” Proceedings simulation of a fair queueing algorithm Proceedings

• f ACM SIGCOMM, 1989.

 Paper is about fair queueing and flow control. Weights are

i d il h l i l di k not mentioned until the last page in a concluding remark.  A. Parekh and R. Gallager, “A generalized processor-

sharing approach to flow control in integrated ar ng appr ac t f w c ntr n nt grat services networks: the single node case” IEEE/ACM

• Trans. on Networking, June 1993.

 Li i

Zh “Vi t l l k t ffi t l

 Lixia Zhang, “Virtual clock: a new traffic control

algorithm for packet-switching networks,” Proc. of ACM SIGCOMM, 1990.

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The end

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